Aim: How do we define the inverse of y = sin x as y = Arc sin x? Do Now: Given f(x) = sin x, a) fill in the table below: b) write the coordinates of each point after reflected in y = x x 0 f(x)f(x) HW: p.424 # 15,21,22,28,29,32,33,37

The coordinates of each point after reflected in y = x are These points are the inverse of y = sin x If we connect those points, the graph is called y = arc sin xor

y = x y = sin x y = arc sin x or

For y = sin x, the Domain = { Real numbers} } Domain = { } real numbers} Range = { Is a function ? Generally NO (It fails the vertical line test)

But if we limit the domain then it can be a function over that particular range. If the domain is the relationIS a function. We use y = Arc sin x or to represent the inverse that is a function. That is, is only limited in quadrants I and IV only

Therefore, y = arcsin x is a function only within - ½π ≤ x ≤ ½π We use y = Arcsin x or y = Sin -1 x to represent Finally, the inverse function of y = sin x only defined in quadrant I and IV

or 150  Which one is true?,since 30  is in quadrant I The idea between the function and inverse function is

is equivalent to Notice that is equivalent to

1.If, write the equivalent function 2. If in degrees., find the value of 3. If, find the value of in radians. 1.If, find the value of in radians. 4. If 5. If, find the value of in radians.

6. Find the exact value of if the angle is a third-quadrant angle. 7. Find the exact value of 8. Find the exact value of 9. Find θ to the nearest degree